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Discriminant_real_part.jpeg‎ (600 × 600 pixel, file size: 66 KB, MIME type: image/jpeg)

La bildo estas kopiita de wikipedia:en. La originala priskribo estas:

Modular discrimnant, real part, as function of nome. (600x600 pixels)

Enhavo

1 Detailed description
2 Source of Image
3 Copyright status
4 Relevant Links
- 4.1 Historio de la dosiero

[redaktu] Detailed description

This image shows the real part of the modular discriminant $\Delta=g_2^3-27g_3^2=(2\pi)^{12}\eta^{24}$ as a function of the square of the nome $q = exp(i πτ)$ on the unit disk |q| < 1. That is, $πτ$ runs from 0 to $2π$ along the edge of the disk. Black areas indicate regions where the real part is zero or negative; blue/green areas where the value is small and positive, yellow/red where it is large and positive. The fractal self-similarity of this function is that of the modular group; note that this function is a modular form. Every modular function will have this general kind of self-similarity.

In the above, g₂=60 G₄ and g₃=140 G₆ are Weierstrass elliptic functions invarients, whereas $η$ is the Dedekind eta function.

See also Image:Gee_three_real.jpeg and Image:Gee_three_imag.jpeg for the real and imaginary parts of g₃.

The imaginary part is quite similar. It, and other related images, can be seen at http://www.linas.org/art-gallery/numberetic/numberetic.html

[redaktu] Source of Image

Created by Linas Vepstas User:Linas <linas@linas.org> on 14 February 2005 using custom software written entirely by Linas Vepstas.

[redaktu] Copyright status

Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.

Permeso estas donita kopii, distribui kaj/aŭ modifi tiun ĉi verkon sub la kondiĉoj de la GNU Free Documentation License, Versio 1.2 aŭ ia ajn alia versio eldonita de la Free Software Foundation; kun neniaj Senvariaj Sekcioj, neniaj Antaŭ-Kovrilaj Tekstoj, kaj neniaj Malantaŭ-Kovrilaj Tekstoj.
Kondiĉe de malgarantioj.

[redaktu] Relevant Links

Weierstrass elliptic functions
Eisenstein series
Q-series

date/time	username	edit summary
03:40, 18 May 2005	en:User:Linas	(<span class="autocomment"><a href="/wiki/Image:Discriminant_real_part.jpeg#Detailed_description" title="Image:Discriminant real part.jpeg">→</a>Detailed description -</span> fix several ommissions)
15:59, 15 February 2005	en:User:Linas	(<span class="autocomment"><a href="/wiki/Image:Discriminant_real_part.jpeg#Detailed_description" title="Image:Discriminant real part.jpeg">→</a>Detailed description</span>)
04:50, 15 February 2005	en:User:Linas	(fix formula)
04:22, 15 February 2005	en:User:Linas	(fix forumula)
04:19, 15 February 2005	en:User:Linas
04:11, 15 February 2005	en:User:Linas	(Modular discrimnant, real part, as function of nome.)

[redaktu] Historio de la dosiero

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.

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(del) (cur) 04:11, 15 February 2005 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 600x600 (67813 bytes) (Modular discrimnant, real part, as function of nome.)

Historio de alŝutoj

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(for) (nun) 18:56, 18. Mar 2006 . . Maksim-bot (Diskuto | kontribuoj) . . 600×600 (67 813 bitokoj) (La bildo estas kopiita de wikipedia:en. La originala priskribo estas: Modular discrimnant, real part, as function of nome. (600x600 pixels) ===Detailed description=== This image shows the real part of the modular discr)